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At a certain car dealership, the 40 vehicles equipped with [#permalink]

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13 Jul 2011, 08:08

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At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

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13 Jul 2011, 08:43

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AnkitK wrote:

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

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23 Jul 2011, 23:18

gaurav1083 wrote:

fluke wrote:

AnkitK wrote:

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

Re: At a certain car dealership, the 40 vehicles equipped with [#permalink]

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24 Jan 2014, 07:32

Is this really a "700+ difficulty" question?It was easy to solve (or to write down all that stuff) though it took me 2min 27sec.Should be a Verbal question with all that writing :D :D
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Thank You = 1 KudosB.Sc., International Production Engineering and ManagementM.Sc. mult., European Master in Management Candidate

Re: At a certain car dealership, the 40 vehicles equipped with [#permalink]

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27 Nov 2017, 05:43

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AnkitK wrote:

At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

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At a certain car dealership, the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. Among all the cars, there are 15 convertibles, 14 of which are equipped with an air-conditioning system. If a customer is willing to purchase either a convertible or a car equipped with air conditioning, what is the probability that a randomly selected vehicle will fit customer specifications?

We are given that the 40 vehicles equipped with air conditioning represent 80% of all cars available for sale. We can let n = the total number of cars and create the following equation:

40 = 0.8n

n = 40/0.8 = 50

Thus, there are a total of 50 cars at the dealership. Furthermore, we are given that there are 15 convertibles, and 14 of them are equipped with air conditioning.

So, the the probability that a randomly selected vehicle will be a convertible or a car with air conditioning is:

[(15 + 40) - 14]/50 = 41/50

Note that we double-counted the 14 cars that are both convertibles and are cars with air conditioning, and so we had to subtract the 14 from the total.
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